Mirzo Ulug`bek nomidagi O`zbekiston Milliy universiteti nafaqat O`zbekistonda, balki Markaziy Osiyoda birinchi va yetakchi oliy ta`lim muassasasi hisoblanadi: 15 ta fakultet, 80 ta kafedra, 16 ta qo‘shma ta’lim dasturi, Bitiruvchilar soni 200 000+

Li simmetriyasi tahlili, giperbolik sistemalarning lyapunov bo‘yicha turg‘unligini tahlil qilish va modellashtirish

Loyiha mavzusi (o‘zbek tilida): Li simmetriyasi tahlili, giperbolik sistemalarning Lyapunov bo‘yicha turg‘unligini tahlil qilish va modellashtiri.
Ilmiy rahbari: Aloyev Raxmatillo Jurayevich
Bajarilish muddati: 04.01.2021-31.12.2023
Loyiha shifri: UZB-Ind-2021-87
Loyiha turi: Amaliy
Kutilayotgan natijalar va ularning ahamiyati: Li guruhi metodi yordamida invariantlik holati, Li simmetriyasi tahlili, cheksiz kichik simmetriyalarning Li algebrasi, simmetrik o‘zgaruvchilar va kvazichiziqli giperbolik sistemalarning simmetrik yechimlarini tadqiq etish. Bundan tashqari, tadqiqot natijalarini samarali tarzda taqdim etish va grafik tasvirlar orqali tushuntirish. Li guruhi hamda giperbolik sistemalarning Lyapunov turg‘unligini tahlil qilish asosida sonli algoritmlar ishlab chiqish. Shuningdek, ushbu sonli usullar yordamida aniq natijalarni o‘rganish uchun olingan natijalarni tahlil qilish. Loyiha doirasida kvazichiziqli giperbolik tenglamalar sistemasi uchun aralash masalaning aniq yechimlari va eksponensial turg‘un sonli yechimini topish uchun Li simmetriyasi tahlili va adekvat hisoblash modeli ishlab chiqish. Li simmetriyasi tahlili va ishlab chiqilgan adekvat hisoblash modelidan beton qoplamasiz sug‘orish kanallarining sug‘orish tizimlarida suv harakatini boshqarishda foydalanish. Li simmetriyasini tahlil qilish va kvazichiziqli giperbolik sistemalarning aralash masalalarini aniq va taqribiy yechish uchun adekvat hisoblash modellarini qurish. Binobarin, hisoblash modellari uchun Lyapunov bo‘yicha ayirmali sxemaning turg‘unligini isbotlash.
Hisobot davrida (loyiha yakunida) qo‘lga kiritilgan muhim natijalar: Bir o‘lchovli chiziqli simmetrik giperbolik sistemalarga qo‘yilgan aralash masalalar bilan ifodalanadigan jarayonlarni tahlil qilindi. O‘zbekiston sharoitida olingan gidrologik va meteorologik ma’lumotlar asosida ushbu masalalarni yechishga doir ma’lumotlarni to‘plandi hamda to‘plangan ma’lumotlar umumlashtirilib, birlamchi qayta ishlandi. O‘zgaruvchan koeffitsiyentli giperbolik sistemalarning turg‘un yechimlarini topish uchun ayirmali sxemalar qurildi va ularning turg‘unligini isbot qilinib Saint Venant tenglamalarini turg‘un yechimlarini topish uchun ayirmali sxemalar tadqiq etildi. Turg‘unligi isbot qilingan sxemalar ustida hisoblash eksperementlari o‘tkazilib, olingan natijalarni vizualizatsiya qilindi. Olingan natijalar nazariy va amaliy xarakterga ega bo‘lib, kelgusida giperbolik sistemalarga qo‘yilgan aralash masalalar uchun ayirmali sxema nazariyasini rivojlantirish uchun xizmat qiladi. Shuningdek elektr energiyasi transporti, ochiq kanallarda suyuqlik oqimi, optik tolalarda yorug‘likning tarqalishi kabi masalalarini sonli yechishda qo‘llanilishi mumkin.
Patent

Loyiha doirasida chop WoS va Scopus bazasidagi xalqaro ilmiy ishlar

  1. Aloev R., Nematova D., Lyapunov numerical stability of a hyperbolic system of linear balance laws with inhomogeneous coefficients. Cite as: AIP Conference Proceedings 2365, 020001 (2021); https://doi.org/10.1063/5.0056862. Published Online: 16 July 2021.
  2. Aloev R., Nematova D., Three-dimensional linear hyperbolic system. Cite as: AIP Conference Proceedings 2365, 020002 (2021); https://doi.org/10.1063/5.0056863. Published Online: 16 July 2021.
  3. Nematova D., Difference upwind scheme for the numerical calculation of stable solutions for a linear hyperbolic system. Cite as: AIP Conference Proceedings 2365, 020003 (2021); https://doi.org/10.1063/5.0057123. Published Online: 16 July 2021.
  4. Eshkuvatov Z., Mamatova H., Ismail Sh., Abdullah I., and Aloev R., Numerical approach for nonlinear system of Fredholm-Volterra integral equations. Cite as: AIP Conference Proceedings 2365, 020010 (2021); https://doi.org/10.1063/5.0057121. Published Online: 16 July 2021.
  5. Khudoyberganov M., An adequate computational model for a mixed problem for the wave equation in a domain with an angle. Cite as: AIP Conference Proceedings 2365, 020027 (2021); https://doi.org/10.1063/5.0057039. Published Online: 16 July 2021.
  6. Khudoyberganov M., Rikhsiboev D., Rashidov J. About one difference scheme for quasi-linear hyperbolic system. Cite as: AIP Conference Proceedings 2365, 020028 (2021); https://doi.org/10.1063/5.0057131. Published Online:16 July 2021.
  7. Akbarova A. Numerical solution of Saint-Venant equations. Cite as: AIP Conference Proceedings 2365, 020026 (2021); https://doi.org/10.1063/5.0056878 Published Online: 16 July 2021
  8. Mamatov A., Bakhramov S., Narmamatov A., An approximate solution by the Galerkin method of a quasilinear equation with a boundary condition containing the time derivative of the unknown function. Cite as: AIP Conference Proceedings 2365, 070003 (2021); https://doi.org/10.1063/5.0057126. Published Online: 16 July 2021
  9. Aloev, R., Berdyshev, A., Akbarova, A., Baishemirov, Z. Development of an algorithm for calculating stable solutions of the saint-venant equation using an upwind implicit difference scheme. Eastern-European Journal of Enterprise Technologies. Tom 4, Vipusk 4, Stranitsi 47 - 56August 2021
  10. Aloev R.D., Eshkuvatov Z.K., Khudoyberganov M.U., Nematova D.E., The Difference splitting scheme for n-dimensional hyperbolic systems» Malaysian Journal of Mathematical Sciences, Malaysian Journal of Mathematical Sciences Scopus, https://mjms.upm.edu.my/current.php 2022. January 2022
  11. Eshkuvatov Z.K., Ismail Sh, Mamatova H.X., Viscarra D.S., Aloev R.D. Modified HAM for solving linear system of Fredholm-Volterra Integral Equations. Malaysian Journal of Mathematical Sciences Scopus, https://mjms.upm.edu.my/current.php. January 2022
  12. R.D.Aloev, S.U. Dadabaev, Stability of the upwind difference splitting scheme for symmetric t-hyperbolic systems with constant coefficients. Results in Applied Mathematics,2022
  13. R.D.Aloev, M.U.Hudayberganov. A Discrete Analogue of the Lyapunov Function for Hyperbolic Systems, Journal Journal of Mathematical Sciences DOI 10.1007/s10958-022-06028-y. 2022